Inertio-capillary cross-streamline drift of droplets in Poiseuille flow using dissipative particle dynamics simulations

Abstract

We find using dissipative particle dynamics (DPD) simulations that a deformable droplet sheared in a narrow microchannel migrates to steady-state position that depends upon the dimensionless particle capillary number , which controls the droplet deformability (with V_max the centerline velocity, μ_f the fluid viscosity, Γ the surface tension, R the droplet radius, and H the gap), the droplet (particle) Reynolds number , which controls inertia, where ρ is the fluid density, as well as on the viscosity ratio of the droplet to the suspending fluid κ = μ_d/μ_f. We find that when the Ohnesorge number is around 0.06, so that inertia is stronger than capillarity, at small capillary number Ca_p < 0.1, the droplet migrates to a position close to that observed for hard spheres by Segre and Silberberg, around 60% of the distance from the centerline to the wall, while for increasing Ca_p the droplet steady-state position moves smoothly towards the centerline, reaching around 20% of the distance from centerline to the wall when Ca_p reaches 0.5 or so. For higher Oh, the droplet position is much less sensitive to Ca_p, and remains at around 30% of the distance from centerline to the wall over the whole accessible range of Ca_p. The results are insensitive to viscosity ratios from unity to the highest value studied here, around 13, and the drift towards the centerline for increasing Ca_p is observed for ratios of droplet diameter to gap size ranging from 0.1 to 0.3. We also find consistency between our predictions and existing perturbation theory for small droplet or particle size, as well as with experimental data. Additionally, we assess the accuracy of the DPD method and conclude that with current computer resources and methods DPD is not readily able to predict cross-stream-line drift for small particle Reynolds number (much less than unity), or for droplets that are less than one tenth the gap size, owing to excessive noise and inadequate numbers of DPD particles per droplet.